Conditional independence tests for count data : Regression conditional independence test for discrete (counts) class dependent variables

Description

The main task of this test is to provide a p-value PVALUE for the null hypothesis: feature 'X' is independent from 'TARGET' given a conditioning set CS. The pvalue is calculated by comparing a Poisson regression model based on the conditioning set CS against a model whose regressor are both X and CS. The comparison is performed through a chi-square test with the appropriate degrees of freedom on the difference between the deviances of the two models. The models supported here are poisson, zero inlftaed poisson and negative binomial.

Usage

testIndPois(target, dataset, xIndex, csIndex, wei = NULL, dataInfo = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
robust = FALSE)
testIndNB(target, dataset, xIndex, csIndex, wei = NULL, dataInfo = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
robust = FALSE)
testIndZIP(target, dataset, xIndex, csIndex, wei = NULL, dataInfo = NULL, 
univariateModels = NULL, hash = FALSE, stat_hash = NULL, pvalue_hash = NULL, 
robust = FALSE)

Arguments

target

A numeric vector containing the values of the target variable.

dataset

A numeric matrix or data frame, in case of categorical predictors (factors), containing the variables for performing the test. Rows as samples and columns as features.

xIndex

The index of the variable whose association with the target we want to test.

csIndex

The indices of the variables to condition on.

wei

A vector of weights to be used for weighted regression. The default value is NULL.

dataInfo

A list object with information on the structure of the data. Default value is NULL.

univariateModels

Fast alternative to the hash object for univariate test. List with vectors "pvalues" (p-values), "stats" (statistics) and "flags" (flag = TRUE if the test was succesful) representing the univariate association of each variable with the target. Default value is NULL.

hash

A boolean variable which indicates whether (TRUE) or not (FALSE) to use tha hash-based implementation of the statistics of SES. Default value is FALSE. If TRUE you have to specify the stat_hash argument and the pvalue_hash argument.

stat_hash

A hash object (hash package required) which contains the cached generated statistics of a SES run in the current dataset, using the current test.

pvalue_hash

A hash object (hash package required) which contains the cached generated p-values of a SES run in the current dataset, using the current test.

robust

A boolean variable which indicates whether (TRUE) or not (FALSE) to use a robust version of the statistical test if it is available. It takes more time than non robust version but it is suggested in case of outliers. Default value is FALSE as it is currently nor supported.

Value

A list including: A list including:

Details

If hash = TRUE, all three tests require the arguments 'stat_hash' and 'pvalue_hash' for the hash-based implementation of the statistic test. These hash Objects are produced or updated by each run of SES (if hash == TRUE) and they can be reused in order to speed up next runs of the current statistic test. If "SESoutput" is the output of a SES run, then these objects can be retrieved by SESoutput@hashObject$stat_hash and the SESoutput@hashObject$pvalue_hash.

Important: Use these arguments only with the same dataset that was used at initialization.

For all the available conditional independence tests that are currently included on the package, please see "?CondIndTests".

If you have overdispersion, the variance is higher than the mean, a negative binomial is to be used.

If you have more zeros than expected under a Poisson model, not overdispersion, then zero inlfated Poisson is to be used.

References

McCullagh P., and Nelder J.A. (1989). Generalized linear models. CRC press, USA, 2nd edition.

Lambert D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34(1):1-14.

Joseph M.H. (2011). Negative Binomial Regression. Cambridge University Press, 2nd edition.

Examples

Run this code


#simulate a dataset with continuous data
dataset <- matrix(runif(400 * 50, 1, 50), ncol = 50 ) 
#the target feature is the last column of the dataset as a vector
target <- rpois(400, 10)
results <- testIndPois(target, dataset, xIndex = 24, csIndex = 10)
results

#run the SES algorithm using the testIndPois conditional independence test
sesObject <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "testIndPois");
sesObject2 <- SES(target, dataset, max_k = 3, threshold = 0.05, test = "testIndNB");
#print summary of the SES output
summary(sesObject);
# plot the SES output
# plot(sesObject, mode = "all");

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